Question

`inte^{2logx}(x^3 + 1)^-1dx` = ____________

Options

• 3log|x³ + 1| + c

• `1/3log|x^3 + 1| + c`

• -3log|x³ + 1| + c

• `-1/3log|x^3 + 1| + c`

Answer 1

`inte^{2logx}(x^3 + 1)^-1dx` =  `underline(1/3log|x^3 + 1| + c)`

Explanation:

Let I = `inte^{2logx}(x^3 + 1)^-1 dx`

= `intx^2/(x^3 + 1)dx`

Put x³ + 1 = t ⇒ 3x² dx = dt

∴ I = `1/3int1/t dt`

= `1/3log|t| + c`

∴ I = `1/3log|x^3 + 1| + c`